Consider the Object-Oriented Languages:
Most people coming from an object-oriented programming background, are familiar with the common and intuitive interfaces in various languages that capture the essence of Java's Collection & List interfaces. Collection refers to a collection of objects which doesn't necessarily have an natural ordering/indexing. A List is a collection which has a natural ordering/indexing. These interfaces abstract many library data-structures in Java, as do their equivalent interfaces in other languages, and an intimate understanding of these interfaces are required to work effectively with most library data-structures.
Transition to Haskell:
Haskell has a type-class system which acts on types analogously to interfaces on objects. Haskell seems to have a well designed type-class hierarchy with regard to Functors, Applicative, Monads, etc. when the type regard functionality. They obviously want correct and well-abstracted type-classes. Yet when you look at many Haskell's containers (List,Map,Sequence,Set,Vector) they almost all have very similar (or identical) functions, yet aren't abstracted through type-classes.
Some Examples:
null for testing "emptyness"length/size for element countelem/member for set inclusionempty and/or singleton for default constructionunion for set union(\\)/diff for set difference(!)/(!!) for unsafe indexing (partial function)(!?)/lookup for safe indexing (total function)If I want to use any of the functions above, but I have imported two or more containers I have to start hiding functions from the imported modules, or explicitly import only the necessary functions from the modules, or qualifying the imported modules. But since all the functions provide the same logical functionality, it just seems like a hassle. If the functions were defined from type-classes, and not separately in each module, the compiler's type inference mechanics could resolve this. It would also make switching underlying containers simple as long as they shared the type-classes (ie: lets just use a Sequence instead of List for better random access efficiency).
Why doesn't Haskell have a Collection and/or Indexable type-class(es) to unify & generalize some of these functions?
Partly, the reason is that monads and arrows are new, innovative features of Haskell, while collections are relatively more mundane. Haskell has a long history as a research language; interesting research questions (designing monad instances & defining generic operations for monads) get more development effort than "industrial-strength" polishing (defining container APIs).
Partly, the reason is that those types come from three different packages (base, containers, and vector), with three separate histories and designers. That makes it harder for their designers to coordinate on providing instances of any single type class.
Partly, the reason is that defining a single type class to cover all five of the containers you mentioned is really hard. List, Sequence, and Vector are relatively similar, but Map and Set have completely different constraints. For List, Sequence, and Vector, you want a simple constructor class, but for Set that won't work, since Set requires an Ord instance on the element type. Even worse, Map can support most of your methods, but its singleton function needs two parameters where the rest need only one.